I must be wrong here, but still want to know where I am wrong. I found the data of Libor rate and swap rate from this link: http://www.interestrateswapstoday.com/libor-rates.html

At the time, I read

USD 6-month Libor rate: L6 = 2.8858%

USD 12-month Libor rate: L12 = 3.1006%

USD 1-year Swap rate: S1 = 2.828%

Then, I calculate

6-month zero bond: P6 = 1/(1 + L6*0.5) = 0.9857762347093784

12-month zero bond: P12 = 1/(1+ L12) = 0.9699264601757894

If above 1-year swap rate is semi-annually settled (this is what I understood, but did not see official explanations), then one shall have

1 = S1*0.5*P6 + (S1*0.5+1)*P12

But, the right hand side is equal to 0.9975800962814657, strictly less than 1. Does it mean there is slight arbitrage opportunity, or otherwise I misunderstood the definition of the rates in the above?

  • 1
    $\begingroup$ The calculations you performed were standard before the financial crisis. Since the crisis, people have come to realize that LIBOR is not a risk-free rate, invalidating these calculations. Simply put, 6m, 12m, and 1y LIBORs embed different credit risks and do not belong to the same curve. Try searching for multi-curve; there are many great discussions over the past decade. $\endgroup$ – Helin Dec 12 '18 at 2:18
  • $\begingroup$ Thanks for your comment, I will search for the multi-curve $\endgroup$ – kenneth Dec 12 '18 at 7:28

Perhaps, but your result could be so close to 1.0000 that exact time each observation is gathered could be a factor. There could be a difference in a matter of seconds or minutes among when these numbers are collected.

Also, your S1 is 3 digits after the decimal and the others have 4. This minor detail could also be cause of it being almost 1.0000 but not exactly.


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